METODOS DE SOLUCIONES ECUACIONES 2 X 2

ALGEBRA

LUZ ENEIDA DAZA

INGRID TATIANA PEREZ

903

INSTITUCION EDUCATIVA FRANCISCO ANTONIO DE ULLOA

2010

SOLUCIÓN

X 3Y 3

X 5Y 1

DESPEJAMOS “X” DE 1

X 3 3Y “3“

SUSTITUYO "3 " EN "2“

X 5Y= 1

3 3Y5Y =1

8Y = 1 3

Y= 4 8 = 12

REEMPLAZO Y = 1/ 2 EN “ 3”

X = 3 3Y

• X +Y = 9• X + 5Y = 25 • Despejamos X en 1• X = 9 – Y• Reemplazo X en 2• 9 – Y + 5Y = 25• -1Y + 5Y = -9 + 25• 4Y = 16 • Y = = 4• Reemplazo Y =4 en• X=9-Y•

• X = 9-4=5

• 5X – Y 9• 2X 4Y 8• Despejamos X de 2• 2x • Reemplazamos X en 1• 5(8-4y) – 2Y = 18• 40- 20Y – 2y = 18• -20Y – 2Y = 18 – 40• -22Y = -22• Y = • Y = 1• Reemplazo Y = 1 en• X= • X = ==2

x+3y =6 5x-2y=13

X= 6 3 13 -2 =-12 -34= -51 1 3 -2 -15 -17 =35 -2

Y= 1 6 5 13

= 13 -30 =-17 = 1 1 3 - 17 -175 -2

5X +7Y =-1 -3X+4Y=-24

X = -1 7-24 4

= (-1) 4-( -24 )7=4+168 = 20 –(-3) 7 = 20 +21

5 7 =164 =4-3 4 41

Y= 5 -1 = 5 (-24 ) – (-1)(-3) -3 -24 41

=-120 -3 = -123 = 3 5 7 41 41

-3 4

• 6x – 5y = -9 • 4x +3y = 13

X= -9 -5 13 3

= (-9 ) 3 –(-5 ) 13 -27 +65 6+3 (-5 ) 4 = 18+ 20

6 -5 4 3 = 92 = 2

38

Y = 6 -9 4 13 =- 78 –(-9) 4 = 78 + 36 = 114 = 338 38 38 38

7x - 15y= 1 -x - 6y = 8

X= 1 -15 8 -6

= ( -6)1 –(-15) 8 = -6 +23 = 29 =0 7 -15 (-15 ) 1 –(-6)7 -15 +42 671 -6

Y= 7 1 1 8

= 1 +56 = 57 =067 67 67

8x + 7Y = 0 4x -21Y=196

X= 0 7 = 0 - 1372 = -1372 =7196 -21 - 168 -28 -196

8 74 -21

Y = 8 – 04 196 = 1568 = -8

-196 -196

3x - 4y =4111x + 6y =47

X = 41 - 447 6 = (41) 6 – (-4) 47= 246 + 1883 -4 3 + 6 (-4) 11 9 - 44

11 6 = 434 = 1235

Y = 3 4111 47 =( 47 )3 – (41) 11= 141 - 451 = -310 = -8

35 35 35 35

9x + 11y= -14-5x + 6y = -34

X = -14 11-34 6 = (-14)6-(-34)11 = 84 +474 9 11 9+ 6 (11) 4 15 +444 6 = 568 = 9

59

Y = 9 -14-5 -34 = (-34)9 –(-14)-5= -306 -70 = 376 =6

59 59 59 59

3x -2y = -6 -7x + 2y =-10

X= 3 -6-7 -10 = (-10) 3 –(-6)-7= -30 -42 3 -2 3+2 (-7) -2 5+14

-7 2 = -72 = -3 19

Y = 3 -2 = (2) 3 –( -7)- 2 = 6 -14 = -8 = 2-7 2 19 19 19

19